Algebra in the Stone-Čech compactification: applications to topologies on groups
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Algebra in the Stone-Čech compactification: applications to topologies on groups
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| Creator |
Protasov, I.V.
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| Description |
For every discrete group G, the Stone-Čech compactification βG of G has a natural structure of compact right topological semigroup. Assume that G is endowed with some left invariant topology I and let τ¯ be the set of all ultrafilters on G converging to the unit of G in I. Then τ¯ is a closed subsemigroup of βG. We survey the results clarifying the interplays between the algebraic properties of τ¯ and the topological properties of (G,I) and apply these results to solve some open problems in the topological group theory. The paper consists of 13 sections: Filters on groups, Semigroup of ultrafilters, Ideals, Idempotents, Equations, Continuity in βG and G∗, Ramsey-like ultrafilters, Maximality, Refinements, Resolvability, Potential compactness and ultraranks, Selected open questions. |
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| Date |
2019-06-14T03:48:18Z
2019-06-14T03:48:18Z 2009 |
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| Type |
Article
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| Identifier |
Algebra in the Stone-Čech compactification: applications to topologies on groups / I.V. Protasov // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 1. — С. 83–110. — Бібліогр.: 62 назв. — англ.
1726-3255 2000 Mathematics Subject Classification: 22A05, 22A15, 22A20, 05A18, 54A35, 54D80. http://dspace.nbuv.gov.ua/handle/123456789/153384 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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